Daniel Juteau (Caen)

(Generalized, modular) Springer correspondence I, II.

Abstract:

In a first part, I will explain the main ideas of the Springer correspondence, which relates irreducible representations of a Weyl group to the geometry of the nilpotent cone in the associated Lie algebra, and some idea of a modular version which I did in my thesis several years ago.

In the second part, I will talk about joint work with P. Achar, A. Henderson and S. Riche where we study a modular analogue of Lusztig's generalization of Springer correspondence. There are induction and restriction functors for perverse sheaves on nilpotent cones, and a notion of cuspidality, like in Harish-Chandra theory. Each cuspidal sheaf on a Levi subgroup gives rise to an induction series, which is parametrized by irreducible representations of a "relative Weyl group". I will say what we know about the classification of cuspidal objects, which is very close to the one for modular representations of finite reductive groups.